Plates - Mechanics of Structures: Variational and Computational Methods - page 820

FIGURE 13.23
Clamped plate with concentrated load. Error in deflection w center at the center of the plate.

FIGURE 13.24
Clamped plate with concentrated load. Error in bending moment at the center of the side.

Fig. 13.26. The displacement and its derivatives with respect to x and y are used as the

DOF at the corner nodes and the derivative of the displacement with respect to the outer
normal of the element boundary is used as the DOF at the center of each side. A complete
5th order polynomial containing 21 unknowns can serve as the trial solution. The principle
of virtual work for the Kirchhoff theory can be used to derive the stiffness matrix. As a
result, a compatible element can be formulated. Other kinds of triangular elements are
introduced in the literature. See, for example, Bazeley, et al. (1965).
The three node DKT and HSM elements can be transformed to four node quadrilateral
elements. One approach is to compose the quadrilateral element using four three node trian-
gular elements. Another approach is to adjust the shape functions of the triangular element
to form the four node quadrilateral elements. For the DKT element, change the shape func-
tions N i in Eq. (13.120) to the shape functions for a quadrilateral element. Equation (13.126)

w